the English translation of
Landry's mail to Lucas
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Paris, 7 July 80
Sir
The number 2^64+1 or 18446744073709551617 is the product of
two factors 67280421310721 and 274177, the latter being prime.
Notice of the result has been sent to the Academy today.
Your advice proved to be ever the wiser, considering that
the smaller factor is relatively small and would require only
about 1000 operations to discover by using the standard method
of successive divisions.
I had set up my calculations with the intention of taking the
process to its end and thus I would be able to announce a result.
There was not much left to do when I unexpectedly came upon the
factor 274177. After such a lengthy process, I could hardly
believe it. The procedure I use first considers the largest
divisors, less than sqrt(N) of course, of the number to be
factored.
One could very well conclude from this that the other factor is
a prime, but besides the possibility that I could have erred
during the course of such a lengthy process, in order to facilitate
my work, I purposely left out divisors of particular forms which
would be easy to deal with separately.
I thank you very much for your interest in this work. This last
14-digit number will allow me to describe the methods that I
use. I hope to arrive for the Congress quite early. Could you
please let me know where I would be able to obtain the pamphlet
where you will mention my work.
My thanks to you
Landry
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This letter was published by Gerardin in
Sphinx-Oedipe(1923) v.18, 70-71
The original letter was written in French.
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source:
1993 Math. Comp., v.61, pages 463-474
Hugh C. Williams: How was F(6) factored?